Simplify the following expression: $ z = \dfrac{-5n}{-6n + 2} + \dfrac{3}{8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-5n}{-6n + 2} \times \dfrac{8}{8} = \dfrac{-40n}{-48n + 16} $ Multiply the second expression by $\dfrac{-6n + 2}{-6n + 2}$ $ \dfrac{3}{8} \times \dfrac{-6n + 2}{-6n + 2} = \dfrac{-18n + 6}{-48n + 16} $ Therefore $ z = \dfrac{-40n}{-48n + 16} + \dfrac{-18n + 6}{-48n + 16} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-40n - 18n + 6}{-48n + 16} $ $z = \dfrac{-58n + 6}{-48n + 16}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{29n - 3}{24n - 8}$